Factor, 28 bytes

[ 2 group [ = ] assoc-all? ] 

Try it online!

• 2 group Split a sequence every 2 elements, e.g. { 1 1 2 2 3 3 } -> { { 1 1 } { 2 2 } { 3 3 } }
• [ = ] assoc-all? Does every pair in a sequence consist of equal values?

Factor, 26 bytes

[ 2 group flip ?first2 = ] 

Try it online!

Thanks to @Bubbler!

• flip Transpose a matrix. e.g. { { 1 1 } { 2 2 } { 3 3 } } -> { { 1 2 3 } { 1 2 3 } }
• ?first2 Get the first 2 elements of a sequence. If there isn't a second one, output f.
• = Are they equal?

Factor, 28 bytes

[ 2 group [ = ] assoc-all? ] 

Try it online!

• 2 group Split a sequence every 2 elements, e.g. { 1 1 2 2 3 3 } -> { { 1 1 } { 2 2 } { 3 3 } }
• [ = ] assoc-all? Does every pair in a sequence consist of equal values?

Factor, 26 24 bytes

[ 2 group flip 1 cut = ] 

Try it online!

Thanks to @Bubbler!
-2 bytes from me

• flip Transpose a matrix. e.g. { { 1 1 } { 2 2 } { 3 3 } } -> { { 1 2 3 } { 1 2 3 } }
• 1 cut Split the matrix in two between its first and second rows. If there isn't a second row, outputs { }. e.g. { { 1 2 3 } { 1 2 3 } } -> { { 1 2 3 } } { { 1 2 3 } }
• = Are they equal?

Factor, 28 bytes

[ 2 group [ = ] assoc-all? ] 

Try it online!

• 2 group Split a sequence every 2 elements, e.g. { 1 1 2 2 3 3 } -> { { 1 1 } { 2 2 } { 3 3 } }
• [ = ] assoc-all? Does every pair in a sequence consist of equal values?

Factor, 28 bytes

[ 2 group [ = ] assoc-all? ] 

Try it online!

• 2 group Split a sequence every 2 elements, e.g. { 1 1 2 2 3 3 } -> { { 1 1 } { 2 2 } { 3 3 } }
• [ = ] assoc-all? Does every pair in a sequence consist of equal values?

Factor, 26 bytes

[ 2 group flip ?first2 = ] 

Try it online!

Thanks to @Bubbler!

• flip Transpose a matrix. e.g. { { 1 1 } { 2 2 } { 3 3 } } -> { { 1 2 3 } { 1 2 3 } }
• ?first2 Get the first 2 elements of a sequence. If there isn't a second one, output f.
• = Are they equal?